A robust and efficient combined trust region–line search exact penalty projected structured approach for constrained nonlinear least squares problems
Speaker: Nezam Mahdavi-Amiri

Time: 9h00, Wednesday, December 18, 2019
Location: Rom 302, Building A5, Institute of Mathematics
Abstract: We describe a combined trust region–line search projected structured algorithm for solving constrained nonlinear least-squares problems. The approach, based on an adaptive projected structured scheme due to Mahdavi-Amiri and Bartels and an exact penalty method due to Coleman and Conn, has been shown to have a local superlinear rate of convergence. For robustness, a new penalty parameter updating strategy and a specific line search technique within the trust region are employed. Technical details of our implementation are discussed and the program is tested on well-known least squares test problems (small and large residuals) as well as some randomly generated test problems due to Bartels and Mahdavi-Amiri. A comparison of our obtained results with the ones obtained by a number of well-known general nonlinear programming methods, while showing outperformance of the algorithm, confirms the practical significance of our adaptive penalty updating scheme, combined trust region–line search strategy, and special structured consideration for the approximate projected least squares Hessians.


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